DECIMALS - YTI Career Institute



DECIMALS

INSTRUCTION SHEET

Addition and Subtraction

Step 1 Line up the decimal points.

Step 2 Put in zeros as placeholders, if necessary.

Step 3 Add or subtract.

Example #1: Example #2:

Step 1- Line up the decimal points.

2.345 + 1.5 ( 2.345 14 – 5.6 ( 14.

+ 1.5__ - 5.6

Step 2 - Put in zeros as placeholders.

2.345 14.0

+ 1.500 - 5.6

Step 3 - Add or subtract.

2.345 14.0

+ 1.500 - 5.6

3.845 8.4

Multiplication

Step 1 Multiply the numbers ignoring the decimals.

Step 2 Add the number of decimal digits in the original numbers.

Step 3 Move the decimal the same number of places to the left in your answer.

Example: 3.2 x 0.41 =

Step 1 - Multiply ignoring the decimal points. 32

X 41___

32

128

1312

Step 2 - Add the number of decimal digits in each of the original numbers: 3.2 has one decimal digit, and 0.41 has two decimal digits. Therefore, the answer will have a total of three decimal digits.

Step 3 - Move the decimal the same number of places to the left in your answer.

1312 will become 1.312

( three places

Division

Step 1 Shift the decimal to the right to make the divisor (outside number) a

whole number.

Step 2 Move the decimal of the dividend (inside number) the same number of

places to the right as the divisor. Add zeros, if needed.

Step 3 Place the decimal point in your answer directly above the new decimal

point in the dividend. Divide.

Example:

Step 1 - Shift the decimal to the right to make the divisor (.45) a whole number.

.45 [pic] becomes 45[pic][pic]

( 2 places

Step 2 - Move the decimal of the dividend (36) the same number of places to the right. Add

zeros if needed.

45[pic] becomes 45[pic]

Step 3 - Place the decimal point in your answer directly above the new decimal point in the dividend. Divide.

45[pic] 45[pic] 360

00

Rounding

Step 1 Determine the place to which the number is to be rounded. Indicate it by

circling it or underlining it.

Step 2 If the digit to the right of the number to be rounded is less than 5, replace it and all the digits to the right of it by zeros. If the digit to the right of the underlined number is 5 or higher, increase the underlined number by 1 and replace all numbers to the right by zeros. If the zeros are decimal digits, you may eliminate them.

Place value chart

Ten thousands |Thousands |Hundreds |Tens |Ones |Decimal Point |Tenths |Hundredths |Thousandths |Ten Thousandths |Hundred Thousandths | |10,000 | 1,000 | 100 | 10 | 1 | . | .1 | .01 | .001 | .0001 |.00001 | |

Example #1: Round 2.832 to the nearest hundredth.

Step 1 – Determine the place to which the number is to be rounded.

2.832

Step 2 – If the digit to the right of the number to be rounded is less than 5, replace it and all the digits to the right of it by zeros. If the digit to the right of the underlined number is 5 or higher, increase the underlined number by 1 and replace all numbers to the right by zeros. If the zeros are decimal digits, you may eliminate them.

2.832 = 2.830 = 2.83

Example #2: Round 43.5648 to the nearest thousandth.

43.5648 = 43.5650 = 43.565

Example #3: Round 5,897,000 to the nearest hundred thousand.

5,897,000 = 5,900,000

Decimal Fractions

To convert a number from fraction form to decimal form, simply divide the numerator (the top number) by the denominator (the bottom number) of the fraction.

Example: 5

8

8[pic] ( Add as many zeros as needed.

48

20

16

40

40

0

Converting a decimal to a fraction

To change a decimal to a fraction, determine the place value of the last number in the decimal. This becomes the denominator. The decimal number becomes the numerator. Then reduce your answer.

Example:

.625 - the 5 is in the thousandths column, therefore,

.625 = [pic] = reduces to [pic]

(Hint: Your denominator will have the same number of zeros as there are decimal digits in the decimal number you started with - .625 has three decimal digits so the denominator will have three zeros)

Order of Operations

When more than one operation is to be performed in a problem, a specific order for solving the problem must be followed.

1. Solve anything in parentheses first

2. Solve anything with an exponent (52 – the 2 is the exponent; it means the number times itself

that many times, so 52 = 5 × 5 = 25)

3. Multiply/Divide from left to right in order

4. Add/Subtract from left to right in order

4.2 + 6(3.8 – 1.1) ÷ 4.5 +.09 =

4.2 + 6(2.7) ÷ 4.5 +.09 =

4.2 + 16.2 ÷ 4.5 +.09 =

4.2 + 3.6 + .09 = 7.89

DECIMALS

PRACTICE SHEET

A. Put the following fractions into decimal form.

1. 1/16 4. 5/32 7. 1⅛

2. 11/8 5. 2 11/32 8. 2 ⅔

3. 2 ⅞ 6. 9/10 9. 12/15

B. Write each of the following decimals in fraction form.

1. 0.5 4. 0.1875 7. 0.1125

2. 0.375 5. 0.88 8. 0.75

3. 0.875 6. 0.975 9. 0.6225

C. Add or subtract as shown.

1. 4.39 + 18.8 = 9. $7.52 + $11.77 =

2. 3.68 – 1.74 = 10. 104.06 – 15.80 =

3. 264.3 + 12.804 = 11. 165.4 + 73.61 =

4. 116.7 – 32.82 = 12. 14 – 6.52 =

5. 3 ¾ + 1.08 = 13. 45.3 – 15.273 =

6. 19.70 + 62.598 = 14. 0.42 + 1.452 + 31.8 =

7. 21 + 3.814 = 15. 3.045 – 1⅛ =

8. 90 – 25.397 = 16. 7.81 – 3.685 =

D. Calculate the following equations.

1. 8.2 × 6.3 = 6. 24.71 × 6.4 =

2. 6.78 × 3.32 = 7. 8.85 × 2.79 =

3. 1.4 × 0.6 = 8. 75.82 × 6.71 =

4. 0.004 × 0.02 = 9. 0.2 × 0.6 × 0.9 =

5. 6.02 × 3.3 = 10. 0.6 × 3.15 × 2.04 =

E. Calculate the following problems, then round to the place indicated.

1. 1.26 ÷ 4.5 = 6. 0.424 ÷ 0.5 =

(tenth) (hundredth)

2. 3.834 ÷ 2.13 = 7. 0.007 ÷ 0.03 =

(tenth) (two decimal digits)

3. 0.04 ÷ 0.076 = 8. 18.76 ÷ 4.05 =

(three decimal places) (one decimal place)

4. 17.8 ÷ 6.4 = 9. 0.08 ÷ 0.053 =

(ten thousandths) (tenth)

5. 17.6 ÷ 0.082 = 10. 1 ¼ ÷ 0.62 =

(thousandth) (hundredth)

F. Solve the problems below following the rules for order of operations.

1. 12.2 × 9.4 – 2.68 + 1.6 ÷ 0.8 = 5. 2.4 + (0.5)2 – 0.35 =

2. 9.6 + 3.6 – (0.4)2 = 6. (1.1)3 + 8.6 ÷ 2.15 – 0.086 =

3. (0.76 + 4.24) ÷ 0.25 + 8.6 = 7. (0.6)3 + (7 – 6.3) × 0.07 =

4. (32.16 – 32.02)2 ÷ (2.24 + 1.76) = 8. (0.6)3 + (2.4)2 + 18.6 ÷ 3.05 + 4.8 =

G. Solve the word problems below.

1. John needed to hang a picture he bought. He drilled a hole ⅜ inch in diameter. The nail he intended to use was 0.5 inch in diameter. Was the hole too small or too large? By how much?

2. Elena’s Hair Salon uses an average of 5.4 quarts of shampoo per month. If Elena wants to order for the year, how many quarts of shampoo does she need to order?

3. XYZ Telephone Company is running an introductory offer on their new long distance program. The program charges a $10.95 initiation fee, then offers the first ten minutes at $.08 per minute with $.05 per minute for any additional minutes. Sylvester decided to purchase the program in June and made long distance calls that month for the following number of minutes: 24, 13, 18, 45, 22, 34, 10, and 15. How much was his monthly bill for his first month of service?

4. Bob has $178.74 in his checking account. He wrote checks for $36.52, $18.92, and $25.93. He also deposited $300.00, $100.00, and $205.16. What is the final balance in Bob’s checking account?

5. A 5/16 inch bolt weighs 0.43 lb. How many bolts are there in a 125 lb. keg?

6. During the first six months of the year, the Busy Bee Printing Company spent the following amounts on paper:

January $470.16 February $390.12 March $176.77

April $200.09 May $506.45 June $189.21

What is the average monthly expenditure for paper?

7. The resistance of an armature while it is cold is 0.028 ohm. After running for several minutes, the resistance increases to 1.340 ohms. Find the increase in the resistance of the armature.

8. When the Better Builder Company completed a small construction job, they found that the following expenses had been incurred: labor, $672.25; gravel, $86.77; sand, $39.41; cement, $180.96; and bricks, $204.35. What total bill should they give the customer if they want to make a profit of $225 on the job?

9. A welder finds that 2.083 cu ft. of acetylene gas is needed to make one bracket. How much gas will be needed to make 27 brackets?

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